Method and apparatus for motion compensation in interferometric sensing systems using a non-linear compensating signal

ABSTRACT

An optical interrogation system, e.g., an OFDR-based system, measures local changes of index of refraction of a sensing light guide subjected to a time-varying disturbance. Interferometric measurement signals detected for a length of the sensing light guide are transformed into the spectral domain. A time varying signal is determined from the transformed interferometric measurement data set. A compensating signal is determined from the time varying signal which is used to compensate the interferometric measurement data set for the time-varying disturbance. The compensation technique may be applied along the length of the light guide.

PRIORITY APPLICATION

This application is a continuation of U.S. patent application Ser. No.14/362,759, filed Jun. 4, 2014, which is the U.S. national phase ofInternational Application No. PCT/US2012/067554, filed Dec. 3, 2012,which designated the U.S. and claims priority from U.S. provisionalpatent application Ser. No. 61/566,860, filed on Dec. 5, 2011, and61/614,662, filed on Mar. 23, 2012, the entire contents of each of whichare incorporated herein by reference.

TECHNICAL FIELD

The technology relates to interferometric sensing applications. Oneexample application is to Optical Frequency Domain Reflectometry (OFDR)sensing applications.

BACKGROUND

Optical Frequency Domain Reflectometry (OFDR) has proven to be aneffective system for measuring strain with high spatial resolution inoptical fiber. See, e.g., U.S. Pat. Nos. 6,545,760; 6,566,648;5,798,521; and 7,538,883. This high resolution capability has provenvery useful in shape sensing applications. See, e.g., U.S. Pat. Nos.7,772,541; 7,781,724; and 20110109898. Simpler strain sensingapplications in single core fiber are described in U.S. PatentApplication 20110247427.

OFDR achieves high spatial resolutions by acquiring data over a widefrequency range as a laser is tuned. In most applications, this tuningtakes place over time as the laser is swept through a range offrequencies. It is assumed using this technique that the fiber undertest is static, or unchanging, during the time of the sweep. If,however, the system being measured varies during the time that the laseris swept, the resulting measurement can be degraded. Such changes can bedue to movement of the fiber under test or movement of the fiber opticleads that connect the fiber under test to the instrument. It would bedesirable to achieve a higher quality measurement in the presence ofsuch time varying changes.

SUMMARY

Example embodiments include methods and an optical interrogation systemfor measuring a parameter of a sensing light guide subjected to atime-varying disturbance. An example time-varying disturbance is motionof the sensing light guide. The optical interrogation system includes anoptical interferometric interrogator and optical detection circuitry,coupled to the optical interferometric interrogator, for detectingoptical interferometric measurement signals for a length of the sensinglight guide. Data processing circuitry receives interferometricmeasurement signals from the optical detection circuitry and generatesan interferometric measurement data set for the length of the sensinglight guide. The interferometric measurement data set is transformedinto the spectral domain, and a time varying signal is determined fromthe transformed interferometric measurement data set. A compensatingsignal is determined from the time varying signal and used to compensatethe interferometric measurement data set for the time-varyingdisturbance to enhance the measurement of the parameter.

In one example implementation, the optical interrogation system is anoptical frequency domain reflectometry (OFDR)-based system that includesan interrogating light source, and wherein the optical interferometricmeasurement signals indicate back scatter amplitude as a function oftime along the sensing light guide.

In a non-limiting embodiment, the processing circuitry determines thetime-varying signal by comparing the interferometric measurement dataset to an interferometric reference data set. Interferometricmeasurement data set is determined for a reflective event in theinterferometric measurement data set and received interferometric datais windowed around the reflective event. The time varying signal may bea phase signal, in which case, the data processing circuitry isconfigured to extract the phase signal from the transformedinterferometric measurement data set by unwrapping the phase signal anddetermine a non-linear signal that describes the time-varyingdisturbance to the sensor by removing a linear fit from the unwrappedphase signal. In this example, the non-linear signal is the compensatingsignal. The data processing circuitry may then subtract the non-linearsignal from the interferometric measurement data set to compensate theinterferometric measurement data set for the time-varying disturbance.

In another example embodiment, where the time varying signal is a phasesignal, the data processing circuitry is configured to extract the phasesignal from the transformed interferometric measurement data in thespectral domain by comparing against a baseline data set in the spectraldomain.

In other example embodiments, the data processing circuitry isconfigured to: divide the interferometric measurement data set intomultiple measurement data segments; transform each of the segments;combine multiple ones of the transformed measurement segments withcorresponding reference spectral data segments; average the combinedsegments; determine a phase response from the averaged segments; anddetermine the time varying signal based on the phase response.Furthermore, the data processing circuitry may be configured todetermine a strain applied to measurement data segments, where thestrain indicates an amount of misalignment between responses of adjacentmeasurement data segments and use the measured strain to align responsesof measurement data segments in the spectral domain.

In another example embodiment, the data processing circuitry isconfigured to compare each data segment to a corresponding referencedata segment in the spectral domain; determine a temporal delay thatindicates an amount of misalignment between reference data segments anddata segments in the temporal domain; and use the measured temporaldelay to align reference data segments and data segments in the temporaldomain.

In an example where the sensing light guide is an optical fiber, whereinthe data processing circuitry may be configured to compensate theinterferometric measurement data set for a strain on the optical fiber.

In a preferred but still example embodiment, the data processingcircuitry is configured to determine motion, temporal delay, and strainalong the sensing light guide and to compensate for accumulated motion,temporal misalignment, and strain along the sensing light guide.

BRIEF DESCRIPTION OF THE DRAWINGS

FIG. 1 is a non-limiting example of an Optical Frequency DomainReflectometer (OFDR)-based sensing system where the sensor experiences atime varying disturbance.

FIG. 2 is a flowchart diagram of non-limiting, example distributedmeasurement procedures using an OFDR system.

FIG. 3 is a plot of the theoretical amplitude vs. optical delay of anideal, single reflection peak as measured using OFDR.

FIG. 4 is a plot of the phase shown in FIG. 3 after being unwrappedshowing a linear phase response.

FIG. 5 is a plot of the amplitude vs. delay from a single reflectorwhere the phase has been distorted during the acquisition sweep by sometime varying change.

FIG. 6 is a plot of the phase vs. optical frequency of the distortedpeak shown in FIG. 5.

FIG. 7 is a non-limiting example diagram showing that a correctionmeasured at point A can correct all subsequent points for disturbancesbetween the measurement point A and the instrument.

FIG. 8 is a plot of the amplitude vs. delay from two reflection eventswhere both peaks are distorted by some time varying phase in the opticalfrequency domain.

FIG. 9 is the plot in FIG. 8 with a window is shown around thereflection peak at index 50.

FIG. 10 shows the window in FIG. 9 showing information only from thefirst reflection peak.

FIG. 11 plots phase distortion calculated from the Fourier transform ofthe windowed data in FIG. 10.

FIG. 12 is a diagram that plots in gray the original distortedreflection peaks in the delay domain and in black the peaks after thedata has been corrected using the phase correction.

FIG. 13 is a flowchart diagram of non-limiting, example procedures forextracting and subsequently correcting for a time varying signal in anOFDR measurement.

FIG. 14 is a flowchart diagram of non-limiting, example procedures forextracting and averaging a time varying phase response in the spectraldomain between a reference OFDR data set and measurement OFDR data set.

FIG. 15 illustrates an example plot of a simulated scatter amplitude vs.delay.

FIG. 16 illustrates a plot of an example phase distortion to be appliedto the scatter data.

FIG. 17 is a graph showing as a black trace the original scatteramplitude vs. delay of the scatter pattern and as a gray trace thescatter amplitude after having been distorted in the frequency domain bythe phase distortion from FIG. 16.

FIG. 18 is a plot of spectral phase distortion calculated from a singledelay domain segment of the scatter pattern.

FIG. 19 is a plot of phase distortion vs. frequency calculated byaveraging complex data from each segment in the spectral domain comparedwith applied phase distortion (gray).

FIG. 20 contrasts an interpolated calculated phase distortion with theoriginal applied phase distortion.

FIG. 21 shows the amplitude of the original scatter pattern and thecorrected scatter pattern.

FIG. 22 plots phase distortion vs. optical frequency for four differentvibrations applied to a fiber lead.

FIG. 23 plots the strain calculated along sensing fiber after vibratingthe fiber at 300 Hz with and without vibration correction.

FIG. 24 plots the strain calculated along the sensing fiber with thefiber draped over an electric fan.

FIG. 25 plots distortion calculated for multiple slices as a function ofwavelength for an unstrained length of fiber.

FIG. 26 shows the phase distortion calculated by averaging the datashown in FIG. 30 as compared with the originally applied phasedistortion.

FIG. 27 shows phase distortion calculated for multiple slices as afunction of wavelength for a strained length of fiber.

FIG. 28 shows phase distortion calculated for multiple slices as afunction of wavelength for a strained length of fiber, where eachsegment has been corrected for the applied strain.

FIG. 29 is a flow chart showing example steps to remove effects of auniform axial strain across the segments used to extract a motioncorrection signal.

FIG. 30 is a graph of phase v. delay showing how an extracted argumentof a complex multiply between a reference and measurement in the delaydomain provides a measure of change in optical delay as a result ofstrain being applied to the measurement.

FIG. 31 is a graph of phase v. delay showing the optical delay responseextracted from the argument of a complex multiplication between areference and corrected measurement.

FIG. 32 illustrate an example feedback process that may be executedalong the length of the fiber correcting for accumulated vibration,accumulated strain, and delay mismatch between the reference andmeasurement segments.

DETAILED DESCRIPTION

The following description sets forth specific details, such asparticular embodiments for purposes of explanation and not limitation.But it will be appreciated by one skilled in the art that otherembodiments may be employed apart from these specific details. In someinstances, detailed descriptions of well known methods, interfaces,circuits, and devices are omitted so as not obscure the description withunnecessary detail. Individual blocks are shown in some figures. Thoseskilled in the art will appreciate that the functions of those blocksmay be implemented using individual hardware circuits, using softwareprograms and data in conjunction with a suitably programmed digitalmicroprocessor or general purpose computer, and/or using applicationsspecific integrated circuitry (ASIC), and/or using one or more digitalsignal processors (DSPs). Software program instructions and data may bestored on a non-transitory, computer-readable storage medium, and whenthe instructions are executed by a computer or other suitable processorcontrol, the computer or processor performs the functions associatedwith those instructions.

Thus, for example, it will be appreciated by those skilled in the artthat diagrams herein can represent conceptual views of illustrativecircuitry or other functional units. Similarly, it will be appreciatedthat any flow charts, state transition diagrams, pseudocode, and thelike represent various processes which may be substantially representedin computer-readable medium and so executed by a computer or processor,whether or not such computer or processor is explicitly shown.

The functions of the various illustrated blocks may be provided throughthe use of hardware such as circuit hardware and/or hardware capable ofexecuting software in the form of coded instructions stored oncomputer-readable medium. Thus, such functions and illustratedfunctional blocks are to be understood as being eitherhardware-implemented and/or computer-implemented, and thusmachine-implemented.

In terms of hardware implementation, the functional blocks may includeor encompass, without limitation, a digital signal processor (DSP)hardware, a reduced instruction set processor, hardware (e.g., digitalor analog) circuitry including but not limited to application specificintegrated circuit(s) (ASIC) and/or field programmable gate array(s)(FPGA(s)), and (where appropriate) state machines capable of performingsuch functions.

In terms of computer implementation, a computer is generally understoodto comprise one or more processors or one or more controllers, and theterms computer, processor, and controller may be employedinterchangeably. When provided by a computer, processor, or controller,the functions may be provided by a single dedicated computer orprocessor or controller, by a single shared computer or processor orcontroller, or by a plurality of individual computers or processors orcontrollers, some of which may be shared or distributed. Moreover, theterm “processor” or “controller” also refers to other hardware capableof performing such functions and/or executing software, such as theexample hardware recited above.

The technology in this application provides an OFDR-based method andapparatus that compensates for sensor motion. The term sensor includesany waveguide to which OFDR-based measurement techniques may be applied.A time varying signal that distorts an OFDR measurement includes anyform of motion of the sensor that occurs over a timescale comparable tothat of the OFDR measurement. A vibration is one non-limiting examplewhile a sudden movement is another. A vibration of constant frequencyand amplitude has a distinct profile in an OFDR measurement whilejarring of the laboratory table during an OFDR measurement has a lessdefined profile. In both cases, the motion can be detrimental to theaccuracy of the intended measurement. Thus, the inventors realized thatan approach must be developed to handle a wide range of movement thatcould be experienced by a given sensor in a deployed sensingenvironment. The term “motion” is used to encompass any type of errorsource that varies the position of the sensing fiber during an OFDRmeasurement.

OFDR is highly effective at performing high resolution distributedmeasurements of a scattering profile along the length of a waveguide.Scattering of light along the waveguide is related to the local index ofrefraction at a given location. Two consecutive measurements can becompared to detect local changes of index of refraction along the lengthof the waveguide by detecting changes in the scattering profile.

FIG. 1 is a non-limiting example setup of an OFDR system 20 used tomonitor local changes of index of refraction along the length of a fiberoptic sensor 10 useful in one or more measurement and/or sensingapplications. In some applications, the fiber optical sensor functionsas a sensor, and in other applications, it may be a device under test(DUT) or other entity. A time varying disturbance or motion 12 is shownimpacting a particular location of the fiber 10 (the term fiber is usedfor convenience, but the technology applies to any suitable waveguide).A tunable light source 30 is swept through a range of opticalfrequencies. This light is split with the use of optical couplers androuted to two separate interferometers. The first interferometer servesas an interferometric interrogator 34 which is connected to the sensingfiber 10. Light enters the sensing fiber 10 through the measurement armof the interferometric interrogator 34. Scattered light along the lengthof the fiber 10 is then interfered with light that has traveled alongthe reference arm of the interferometric interrogator 34. The secondinterferometer within a laser monitor network 32 measures fluctuationsin the tuning rate as the light source 30 scans through a frequencyrange. The laser monitor network 32 also contains a Hydrogen Cyanide(HCN) gas cell which is used to provide absolute wavelength referencethroughout the measurement scan. A series of optical detectors 40converts detected light signals from the laser monitor network 32, gascell HCN, and the interference pattern from the sensing fiber 35 intoelectrical signals for a data acquisition unit 36. A data processor 28uses the acquired electrical signals from the data acquisition unit 36to extract a scattering profile along the length of the sensor 10 as isexplained in more detail in conjunction with FIG. 2.

FIG. 2 is a flowchart diagram of non-limiting, example distributedmeasurement procedures using an OFDR system. In step S1, the tunablelight source is swept through a range of optical frequencies anddirected into the sensor 10 via the measurement arm of theinterferometric interrogator (step S2). Scattered light along the lengthof the sensor 10 interferes with light that has traveled through thereference path of the interferometric interrogator. An absolutewavelength reference is provided for the measurement scan (step S3), andtuning rate variations are measured (step S4). Optical detectors convertdetected optical signals into electrical signals (step S5) forprocessing by the data processor 28. The interference pattern of thesensing fiber is preferably resampled using the laser monitor signal toensure the detected signals are sampled with a constant increment ofoptical frequency (step S6). Once resampled, a Fourier transform isperformed to produce a sensor 10 scatter signal in the temporal domain.In the temporal domain, the scatter signal depicts the amplitude of thescattering events as a function of delay along the length of the sensor10 (step S8). Using the distance light travels in a given increment oftime, this delay is converted to a signal measure of length along thesensor 10. In other words, this signal depicts each scattering event asa function of distance along the sensor 10. The sampling period isreferred to as the spatial resolution and is inversely proportional tothe frequency range that the tunable light source was swept throughduring the measurement.

As the sensing fiber 10 is strained, local scatters shift as the fiberchanges in physical length. It can be shown that these distortions arehighly repeatable. Hence, an OFDR measurement can be retained in memorythat serves as a reference pattern of the fiber in an unstrained state.A subsequent measurement can be compared to this reference pattern togain a measure of shift in delay of the local scatters along the lengthof the sensing fiber. This shift in delay manifests as a continuous,slowly varying optical phase signal when compared against the referencescatter pattern. The derivative of this optical phase signal is directlyproportional to change in physical length of the sensing core. Change inphysical length can be scaled to strain producing a continuousmeasurement of strain along the sensing fiber 10.

As detailed above, during an OFDR measurement the optical interferencebetween a reference path and a measurement path is recorded as a laseris swept through a range of optical frequencies. The resultinginterference pattern at the optical detectors of the system containsinformation about both the amplitude and the phase of the lightreflected from the sensing fiber. The phase and amplitude of the lightis recorded as a function of time through the laser sweep. A basicassumption of the system is that the interferometer system underinterrogation, which includes the sensing fiber 10, does not changeduring the sweep, and that the phase and amplitude response of thesystem as a function of optical frequency is encoded in time as thelaser is swept. Therefore, if the laser frequency is known as functionof time, the phase and amplitude response of the system are known as afunction of laser wavelength.

But if the system is not stationary during a measurement, themeasurement is distorted. Consider for example the response of a singlereflection as the laser is swept linearly with time. This singlereflection event results in sinusoidal interference fringes at thedetection electronics. The Fourier transform of the interference signalfrom a single reflector gives a single clean peak as a function ofoptical delay. FIG. 3 plots a theoretical amplitude vs. optical delay ofan ideal, single reflection peak as measured using OFDR.

The position of the reflection in delay is proportional to the magnitudeof the phase slope in the spectral domain. Further, by definition, anideal reflection from a single event in the temporal domain has a linearphase slope in the spectral domain. As an example, the spectral domainphase is plotted “unwrapped” in FIG. 4. Unwrapping can be thought of aslight moves along a fiber, the optical phase increases. In the complexplane, as the phase increases and moves around the unit circle, it makesone revolution and continues on the next. Unwrapping the phaseeffectively linearizes this revolving phase signal by keeping track ofthe total number of complete revolutions to gain a measure of the totaloptical phase change.

Now consider the case where the optical delay between the reflection ofthis event and the beam recombination in the interferometer changes,i.e., where the phase has been distorted by some time varying change asthe laser is swept. As shown in FIG. 5, this results in an additionalphase modulation on the measured interference signal. In the presence ofthis time-dependent phase modulation, the resulting Fourier transform ofthe interference signal is distorted as illustrated in FIG. 5. The peakis no longer “clean,” with noise appearing around the base of the peak.

FIG. 6 plots the phase vs. optical frequency of the distorted peak shownin FIG. 5. The spectral domain phase of this distorted peak shows smalldepartures from linear phase. These deviations from linearity indicatethat the position of the sensing fiber was not constant as the OFDRsystem performed a measurement. These deviations from a linear phaseresponse in the spectral domain, and the resulting distortion of theideal peak are problematic for distributed strain measurements. Asdescribed above, a distributed OFDR strain measurement is compared to abaseline reference scan of the sensing fiber, e.g., by performing across correlation. Distortion of a measurement as a result of motion ofthe sensor greatly diminishes the accuracy of this comparison. Theinventors recognized this problem and developed technology to compensatefor the effects of motion from a measurement to improve the accuracy ofOFDR measurements.

As a starting point to the solution, the inventors recognized that thefundamental nature of an OFDR measurement allows efficient and effectiveremoval of motion effects from an OFDR measurement. During OFDRacquisition, the magnitude of the phase response in the spectral domainfrom an ideal, single reflective event in the delay domain isproportional to the delay of that event. Thus, the phase modulation mustbe additive along the length of the sensor. In other words, the phasemodulation seen by any point in the fiber is the sum of all of the phasemodulations in the fiber before the point of interest. This means thatmeasuring the phase modulation at any one point in the optical fiberprovides an ability to correct for these modulations along the remainingportion of the fiber.

FIG. 7 is a diagram showing that a correction measured at point A cancorrect all subsequent points for disturbances between the measurementpoint A and the OFDR instrument. In other words, by measuring motion ata point A in the sensing fiber 10, all effects of motion between thepoint A and the instrument may be corrected for the remaining length ofthe sensor 10. Hence, a measurement at point B will no longer beaffected by the motion distortion before point A. This concept isfurther illustrated in FIG. 8 by observing the distortion of thereflections at both point A and point B in the delay domain due to atime varying distortion before point A. The peaks have both beendistorted by some time varying phase in the optical frequency domain.

If it is known there is only a single reflection at or around index 50,then the complex data set associated with this reflection, i.e., thepoints from zero to 100, may be used to characterize the vibrations(phase modulations) that occurred leading up to this reflection.Removing these vibration effects from the data set removes thatdistortion as observed in both reflective events at point A and point Balong the fiber 10.

In this case, vibration information from the first peak is obtained bywindowing around that peak as shown by the rectangular window centeredaround the reflection peak at index 50 in FIG. 9. After themultiplication, no information from the other peak remains. Recall thatthe information contained in these first 100 points is complex valuedcontaining both phase and amplitude information. The correspondingamplitude data after the windowing operation is depicted in FIG. 10where the window is multiplied with the data acquired from the tworeflections resulting in a complex data set only from the firstreflection peak. This windowed complex data set is Fourier transformedin order to extract the phase distortion in the spectral domain. Thisphase distortion describes the non-linearity associated with phaseresponse from the original ideal, single reflection at point A and isdepicted in FIG. 11.

This phase distortion is then used as a phase distortion correctionwhich may be applied to the entire acquired data set by subtracting thisphase distortion from the measured phase for the entire acquired dataset to recover clean peaks at both locations in the delay domain. Thisis shown in FIG. 12 where the gray lines shows the original distortedreflection peaks in the delay domain and the black line shows the peaksafter the data has been corrected using the phase correction calculatedfrom the peak at index 50. Both peaks are now sharp.

A flowchart outlining non-limiting, example steps to extract the timevarying signal as a result of motion and the subsequent correction ofthe data is shown in FIG. 13. Starting at step S10, a windowingoperation is performed on a complex valued OFDR data set in the timedelay domain about a reflective event, e.g., at the beginning of thedata set. An inverse Fourier transform is applied to transform the dataset into the frequency domain (step S12). The phase response in thespectral domain is extracted by unwrapping the phase signal (step S14).The total accumulated phase is proportional to the location of thereflective event in the delay domain. Each index of delay in the delaydomain accumulates a two Pi phase change in the spectral domain, e.g., areflective event at index 500 will have a total accumulated phaseresponse in the spectral domain of 1000 Pi after unwrapping. Subtractinga linear fit from this accumulated phase response removes the phaseassociated with the location of the reflective event in the delay domainproviding a measure of the non-linear time varying signal that describesthe motion of the sensor (step S16). The non-linear time varying signalis a compensating signal, which for example, is subtracted from thephase of the original measurement OFDR data set in the spectral domain(step S18). The motion-compensated spectral response is then transformedinto the time delay domain using a Fourier transform operation (stepS20), which may be used to identify and/or display a clean spectral peakfor the reflection.

This example process removes or at least substantially reduces theeffects of motion on an OFDR measurement by extracting a time varyingsignal up to a point in the sensor fiber 10, and then using this signalto compensate the data produced along the length of the sensor 10. Thistechnology compensates for one or multiple movements along the length ofthe sensor fiber 10 and ensures robustness for a wide range ofenvironments for a deployed sensor in various OFDR applications.Additional non-limiting example embodiments are now described.

A common type of fiber in OFDR sensing applications is industrystandard, low bend loss fiber that has a Rayleigh scatter profile. TheRayleigh scatter profile of a given length of sensor fiber appears as arandom, broadband signal and results from light scattering off the glassmolecules of the fiber itself. This scattering pattern is highlyrepeatable and may be considered a physical property of a given sensor.Thus, this scattering “fingerprint” is used to obtain a baseline orreference measurement of the fiber.

In the example case of a single reflective event, a linear fit wasremoved from the phase response in the spectral domain to isolate thenon-linear component that captured the effects of motion on themeasurement. In a practical system, ideal single reflective eventstypically do not occur and the spectral responses of neighboringreflective events will mask the desired non-linear component. This canbe overcome by comparing a measurement of the fiber to a baselinemeasurement of the same fiber. The scattering profile of the fiber ishighly repeatable, and the comparison of a segment of the measurement inthe spectral domain to the corresponding segment of the baseline scan inthe spectral domain will allow one to isolate the effects of motionduring the measurement. In other words, if no motion is present during ameasurement, the comparison of the measurement and baseline in thespectral domain will produce a zero valued phase difference. If motionis present, a non-linear response will be observed.

Three problems must be overcome. First, Rayleigh scatter is a weaksignal, and thus, the compensation for motion is susceptible to noise.The inventors developed an averaging methodology to increase therobustness of the motion compensation. Second, deployed sensors aresusceptible to many different environmental factors. Robust motioncompensation should ensure that changes in the environment, such astemperature changes, do not reduce the effectiveness of thecompensation. The inventors developed a way to remove the effects ofaxial strain from the motion extraction region. Third, there is noguarantee that a deployed sensor only experiences a time varyingdisturbance before the region of interest in the sensing fiber. Thus,the compensation technology should operate along the length of thesensor to systematically remove various motion affects along the lengthof the sensor.

The low signal level of Rayleigh scatter problem is solved using anaveraging operation for the scatter from multiple adjacent segments inthe fiber. In typical applications, it can be assumed that the effectsof motion are similar for short lengths of sensing fiber. Choosing smallsegments of sensing fiber in the delay domain permits the assumptionthat the adjacent segments will have observed a similar time varyingdistortion. First, the time varying spectral distortion is extractedfrom each segment. Fourier transforming both the measurement OFDR datafor a segment and the reference/baseline OFDR data for that same segmentto the spectral domain, the complex valued spectral data can be comparedto extract a measure of the phase distortion as a result of motion inthe measurement segment. This process may be repeated for each adjacentsegment, and the average of the spectral distortions calculated. Examplesteps for such a process are described in the flow chart in FIG. 14.

OFDR scans of the sensing fiber are performed on the sensing fiber 10 ina baseline environment (e.g., no motion, controlled temperature, etc.affecting the fiber) (step S33) to produce OFDR reference data for eachof multiple segments of the fiber (step S34) and in an application abaseline environment (e.g., where there may be motion, temperaturechanges, etc. affecting the fiber) (step S30) to produce OFDRmeasurement data for each of multiple segments of the fiber (step S31).Segments may be partitioned using for example the windowing techniquedescribed above. A Fourier transform operation is performed on the eachof the measurement segments (step S32) and on the each of the referencesegments (step S35) to transform the segment data into the spectraldomain. One example way to perform the Fourier transform is using a fastFourier transform (FFT). Then, the measurement spectral data for eachsegment is complex multiplied (the data is complex) with the complexconjugate of the reference spectral data for each corresponding segment(step S36) Mathematically, the multiplication of a complex valued signalwith the conjugate of a second signal is equivalent to calculating thedifference in the phase values of the complex signals. Due to the noisethat distorts this phase measurement, it is desired to average adjacentsegments. To average adjacent segments, the real and imaginarycomponents of the complex products from adjacent segments averagedrespectively (step S37). The average phase response is extracted bycalculating the arc tangent of the real and imaginary parts of theaveraged complex product. This phase difference is subsequentlyunwrapped as described above. This phase response can then be used tocompensate for the distortions as a result of motion. As an example, thephase response could be linearly interpolated to match the size of themeasurement and subtracted from the spectral domain of the originalmeasurement data to remove the effects of motion.

Although two parallel tracks are shown in steps S30-S32 and S33-S35,these steps need not be performed in parallel, at the same general time,or even one for one. For example, the reference scan steps S33-S35 maybe performed in advance and the reference segment data stored in memoryfor subsequent use with measured segment data. One measurement scan isshown, but it will be appreciated that steps S30-S32 and S36-S39 may berepeated for one or more other measurement scans.

The processing flow for the calculation of the motion compensation shownin FIG. 14 is now described mathematically. Let κ_(p) be the array ofcomplex scatter measurements in a length of uniformly strained fiber,where p indicates the position along the array in delay. A set ofsub-arrays is produced by transforming successive segments of κ_(p) backinto the spectral domain. K_(kn) represents the spectrum of measurementsegment n and k is the spectral index:K_(kn) =FFT{κ_(nS) . . . κ_((n+1)S)},where S is the length in number of points of the segment. The process isrepeated using the reference measurement, η_(p),N_(kn)=FFT{η_(nS) . . . η_((n+1)S)}The signal that captures the effects of motion is then given by,

$v_{k} = {{\angle{\sum\limits_{n}\;{N_{kn}^{*}K_{kn}}}} = {\angle{\sum\limits_{n}\;{{FFT}{\{ {\eta_{nS}\mspace{14mu}\ldots\mspace{14mu}\eta_{{({n + 1})}S}} \}^{*} \cdot {FFT}}\{ {\kappa_{nS}\mspace{14mu}\ldots\mspace{14mu}\kappa_{{({n + 1})}S}} \}}}}}$

An example of the above is now described using synthesized data. Anarbitrary scatter pattern is generated as shown in FIG. 15 which plotssimulated scatter amplitude vs. delay. Next, FIG. 16 shows an examplephase distortion (a motion error that is low in frequency content) to beapplied to the scatter data. This phase disturbance is applied to thespectrum of the scatter data by first transforming the complex scatterdata into the spectral domain and then multiplying transformed scatterdata by a complex array that has the phase disturbance as its argumentand an amplitude of one. The resulting scatter pattern is significantlyaltered as shown in FIG. 17. The black trace shows the original scatteramplitude vs. delay, and the gray trace shows the scatter amplitudeafter having been distorted in the frequency domain.

In order to extract the effects of motion, eight (8) segments ofthirty-two (32) points, or 256 points total, are transformed from thedelay domain and into the spectral domain. This segmenting andtransforming is performed on both the altered data serving as themeasured data set and the reference data set. FIG. 18 plots the spectralphase distortion calculated from a single delay domain segment of thescatter pattern shown. The gray dots represent the phase distortionapplied to this segment. The black dots represent the phase distortionas calculated comparing the distorted segment data to the referencedata. One can see frequencies at which the calculated phase distortiondoes not match the applied phase distortion. For example, the phasedistortion for index 4 is significant.

However, when the relative complex spectra are averaged, the influenceof each individual phase value may be effectively weighted by the sizeof the amplitude at that location. FIG. 19 plots phase distortion vs.frequency calculated (black) by averaging the relative complex data fromeach segment in the spectral domain compared with applied phasedistortion (gray). The averaging provides a much more accuratemeasurement of the phase as can be seen by comparing FIG. 18 with FIG.19.

Averaging over adjacent segments provides a good estimate of the errorsignal caused by fiber motion present in the measurement data. The nextstep is to apply the inverse of this phase to the entire scattermeasurement data to compensate the measurement data, and then invert thecompensated measurement scatter data back into the delay domain. Beforedoing this, a signal is generated having the same size as the originalmeasurement data set (in this case a size of 2048 points) rather thanthe length of the segment being analyzed. This can be performed, forexample, by mathematically interpolating the calculated error signal tomatch the size of the measurement using a Fourier Interpolation. AFourier Interpolation is a standard mathematical means of interpolatinga signal of a given array size to a desired array size. Briefly, aFourier Interpolation is performed by first taking the Fourier Transformof a real valued signal. In the transform domain, the data is zeropadded by placing zeros in the center of the data array until the arrayis the size of the desired interpolated array size. An inverse Fouriertransform is then performed on the zero padded data. The real componentof this complex signal will be a scaled interpolation of the originalreal valued signal. The amplitude of this signal is then scaled by theratio of the interpolated array size to the size of the original realvalued array.

Once we have interpolated the phase estimate, it can be compared to theoriginally applied phase disturbance, shown in gray in FIG. 20 with thephase estimate in the thin black line. The gray is the original appliedphase distortion. The two match relatively well.

Applying this interpolated phase estimate to the scatter spectrum andrecalculating the scatter as a function of distance recovers theoriginal signal. This is shown in FIG. 21 where the black trace is theamplitude of the original scatter pattern generated and the grey traceis the amplitude of the corrected scatter pattern calculated asdescribed above.

The example synthesized data embodiment described and illustrated abovewas implemented in an OFDR system that was then used to detect strain inthe sensing fiber beyond the motion compensation region. FIG. 22 plotsthe phase distortion vs. optical frequency calculated as described abovefor four different vibrations applied to a fiber lead. The first threewere generated with a speaker at 100, 200, and 300 Hz. In the fourth,the lead was draped over an electric fan to generate a representativeenvironmental perturbation. In the first three, the increasing vibrationfrequency is clearly distinguishable. If these vibrations are notcompensated, the determination of strain is not accurate as shown by thegray trace in FIG. 23. With the phase distortion corrections applied,however, the errors do not occur, as shown by the black trace in FIG.23. The trace in FIG. 23 includes strain data taken with the 300 Hzvibration present with and without phase distortion corrections.

FIG. 24 plots the strain calculated along the sensing fiber with thelead draped over the electric fan. Even though this disturbance to thesensor is more severe, (see the uncorrected gray data with many failedstrain calculations), the correction is still effective as shown by theblack trace.

Other aspects of the technology relates to robustness. The inventorsdeveloped a way for the phase distortion compensation described above towork successfully in different environments. If there is a strainpresent in the optical fiber length used for vibration calculation, theeffect is an accumulation of a phase difference between segments in thespectral domain. This phase difference modifies the response in thespectral domain, making it difficult to extract an averaged responsethat captures the effects of motion. In this case, the inventorsdetermined that it is desirable to “align” the segments in the spectraldomain.

The example synthesized data embodiment above permitted adding thecomplex segments together because, with no strain present, they each hadthe same phase relative to the reference data set. An estimate of thephase change between segments in the spectral domain may be calculatedby first multiplying each segment by the conjugate of the previoussegment. Note, this is a comparison of the phase response between eachsegment in the average series, and is not referenced to the baselinescan of the fiber. Thus, any distortion due to vibration will beminimized as each measurement segment is similar to the next segment. Ifthere are 10 segments, then there will be 9 product segments. The phaseof each of the elements of the product is the average change in phasebetween segments, which is a measurement of the strain. Since everyelement contains the same phase (plus some noise), all of the elementsmay be summed, and the phase of this complex sum will be the averagephase increment between segments. So in the example of 10 segments thatare 32 elements in length, 288 complex numbers are summed to obtain theaverage phase increment between segments.

Returning to the original analysis where κ_(p) is the array of complexscatter measurements in the length of uniformly strained fiber, a set ofsub-arrays is constructed by transforming successive segments of κ_(p)back into the spectral domain (k)K_(kn)=FFT{κ_(nS) . . . κ_((n+1)S)},where S is the length in number of points of the segment. The process isrepeated using the reference measurement, η_(p),N_(kn)=FFT{η_(nS) . . . η_((n+1)S)}

The average phase difference between successive segments, δ, iscalculated, where,

$\delta = {\angle{\sum\limits_{n}\;{\sum\limits_{k}\;{( {N_{k{({n + 1})}}^{*}K_{k{({n + 1})}}} )( {N_{kn}K_{kn}^{*}} )}}}}$

The correction may then be applied to the calculation of the vibrationby applying linearly increasing phase shifts to each segment.

$v_{k} = {\angle{\sum\limits_{n}\;{e^{{- i}\;\delta\; n}N_{kn}^{*}K_{kn}}}}$

Alternately, the strain can be applied to the original complex arraysprior to the calculations of the spectral segments.

$N_{kn}^{\prime} = {{FFT}\{ {e^{i\frac{\delta}{S}{nS}}\eta_{nS}\mspace{14mu}\ldots\mspace{14mu} e^{i\frac{\delta}{S}p}\eta_{p}\mspace{14mu}\ldots\mspace{14mu} e^{i\frac{\delta}{S}{({n + 1})}S}\eta_{{({n + 1})}S}} \}}$

This advantageously introduces any significant spectral shift to thetransform data prior to the spectral computations. The vibration iscalculated as before using the modified reference in this instance.

$v_{k} = {{\angle{\sum\limits_{n}\;{N_{kn}^{\prime*}K_{kn}}}} = {\angle{\sum\limits_{n}\;{{FFT}{\{ {\eta_{nS}\mspace{14mu}\ldots\mspace{14mu}\eta_{{({n + 1})}S}} \}^{*} \cdot {FFT}}\{ {\kappa_{nS}\mspace{14mu}\ldots\mspace{14mu}\kappa_{{({n + 1})}S}} \}}}}}$

To illustrate this concept, consider the previous example that operatedon simulated Rayleigh scatter data. FIG. 25 plots phase distortioncalculated for multiple segments as a function of wavelength for anunstrained length of fiber. The phase difference calculated for each ofthe segments under the condition of zero strain provides a tightgrouping of phase curves, and the complex numbers may be averageddirectly to get the average phase at every point. In other words,averaging the complex values for an unstrained fiber subjected tomovement produces a good representation of the original phase error.Now, strain is added to the original computational model by adding alinear phase term to the original scatter data.

FIG. 26 plots phase distortion calculated by averaging the data shown inblack against the originally applied phase distortion shown in gray.After introducing a strain to the fiber, the spectral responses of thesegments are no longer tightly bunched as shown in FIG. 27 which plotsphase distortion calculated for multiple segments as a function ofwavelength for a strained length of fiber. In other words, the phaseresponse at each frequency no longer match for each segment so a simpleaverage no longer works to recover the vibration signal as thepopulation of points has too much variation. As a result, this signalwill not average to the phase distortion observed in FIG. 26.Accordingly, there needs to be a correction for the strain.

A strain applied to the sensor will manifest as a shift in the spectraldomain and also as a change in the phase slope in the temporal domainwhen compared to a baseline scan in an OFDR measurement. Generating astrain correction from the average difference in phase between themeasurement segments in the spectral domain gives a measure the phaseslope applied in the temporal domain. With this measure of strain, anopposite phase slope is applied across the segments in the temporaldomain to realign the responses of the segments in the spectral domainas seen in FIG. 28, where each segment has been corrected for theapplied strain. The data once again match.

Example procedures removing or at least reducing the effects of auniform axial strain across the segments to extract a motioncompensation signal are outlined in the flow chart in FIG. 29. OFDRmeasurement data in the temporal domain for each of a series of fibermeasurement segments are defined (steps S40). Each segment data set isFourier transformed into the spectral domain (step S41). A spectraldomain product of the measurement segment data set and the complexconjugate of an adjacent measurement segment data set is calculated(step S42). The argument of the complex comparison is defined as thearctangent of the ratio of the imaginary and real values of a complexnumber. The resulting argument is then averaged across the number ofpoints within the segment in order to produce an average phase incrementfor that pair of segments (step S43). The average change in phasebetween a pair of segments is referred to as the phase increment. Theresulting phase increments across each pair of compared measurementsegments are averaged (step S44). The averaged phase increment isdirectly proportional to the uniform axial strain across the originalmeasurement segments and the average phase increment is scaled to ameasure of strain (step S45). This strain value defines the slope of thephase correction to be applied in the temporal domain to align segmentsin the spectral domain. A correction is applied in the temporal domainby multiplying the data with a generated complex correction with thephase slope based on the measured strain and with an amplitude of one(step S46).

An example optical phase response as result of strained measurement ispresented in FIG. 30 which shows that the slope of the optical phaseresponse extracted between a measurement and reference length of fiberin the delay domain has a slope. Using the method in FIG. 29, a measureof this slope is extracted by comparing the difference between themeasurement segments in the spectral domain. To remove the strain fromthe measurement, a phase response opposite in slope is applied acrossthe measurement length. If the reference and measurement are once againcompared by extracting the argument of their product in the temporaldomain, a zero slope optical delay response is observed. FIG. 31 showsthe optical delay response extracted from the argument of a complexmultiplication between a reference and corrected measurement. After thiscompensation for strain in the temporal domain, the responses in thespectral domain are generally aligned and can be averaged to gain a moreaccurate measure of the distortion as a result of motion.

It has been shown that a length of fiber can be selected in order toextract the spectral distortion as a result of motion experienced by thesensor up to that location. This calculation may be made more robust bydividing that length of fiber into smaller segments and averaging thespectral distortion across those segments. In the presence of a uniformaxial strain on the fiber, this strain can be measured and removed bycomparing the responses of the measurement segments in the spectraldomain. Another aspect of the technology relates to ensuring robustnessover a wide range of applications.

So far, it is assumed that the reference segments and the measurementsegments are aligned in temporal delay. If axial strain is present inthe sensor leading up to the location that a motion distortion isdesired to be measured, then the measured sensor may have an overallchange in length. As a result, some mechanism is needed to ensure thatthe OFDR measurement data for a physical segment of the fiber iscompared to the OFDR reference or baseline data for the same physicalsegment. It will be shown that a signal from the data can be extractedthat indicates how misaligned a measurement and reference segment are inphysical distance during the extraction of the spectral response. Withthis measure of alignment in physical distance, the segment data setsmay be realigned so that an accurate measurement of the spectral phasedistortion as a result of motion may be determined.

Taking a step back from this problem, the inventors observed that boththe effects of axial strain and vibration accumulate along the length ofthe sensing fiber. However, in a wide range of applications, both therate of accumulation of vibration and change in axial strain are slowlyvarying across a small length of the sensor. As mentioned already,robust vibration correction includes segmenting a length of fiber intosmaller segments for averaging, ensuring that these segments aretemporally aligned with the same physical segments in the baselinemeasurement, and removing the strain present across the segments. Sinceboth axial strain and vibration are slowly changing, a routine may beexecuted along the length of the fiber that measures small changes intemporal delay, axial strain, and vibration along the length of thesensor and accumulates these changes. Hence, a feedback loop of sorts isestablished as the algorithm advances along the length of the fiber.

A property of the Fourier transform may be used to measure the temporaldelay between a reference and measurement segment. If the reference andmeasurement are not aligned in the delay domain, then a slope manifestson the phase response in the spectral domain. Thus, one can detect ifthe reference and measurement are misaligned by extracting the argumentof the product between the reference and measurement segment in thespectral domain. In other words, the deviations of the spectral phaseresponse from linearity capture the distortions as a result of motion,and the slope of this phase response is an indicator of how misalignedthe reference and measurement segments are in the delay domain. This isdescribed by the following mathematical analysis:

A delay in the time domain is a linear phase term in the frequencydomain as shown with Eq. 1, Eq. 2, and Eq. 3.

$\begin{matrix}{{f(t)} = {\frac{1}{2\pi}{\int_{- \infty}^{\infty}{{F(\omega)}e^{{- i}\;\omega\; t}d\;\omega}}}} & {{Eq}.\mspace{14mu} 1} \\{{f( {t + {\Delta\; t}} )} = {\frac{1}{2\pi}{\int_{- \infty}^{\infty}{{F(\omega)}e^{{- i}\;{\omega{({t + {\Delta\; t}})}}}d\;\omega}}}} & {{Eq}.\mspace{14mu} 2} \\{{f( {t + {\Delta\; t}} )} = {\frac{1}{2\pi}{\int_{- \infty}^{\infty}{e^{{- i}\;{\omega\Delta}\; t}{F(\omega)}e^{{- i}\;\omega\; t}d\;\omega}}}} & {{Eq}.\mspace{14mu} 3}\end{matrix}$

With a measure of vibration, temporal misalignment, and strain across alength of sensing fiber, a feedback loop can be established thatadvances along the length of the sensing fiber. An example,computer-implemented feedback algorithm is depicted in FIG. 32 that maybe executed along the length of the fiber correcting for accumulatedvibration, accumulated strain, and delay mismatch between the referenceand measurement segments. First, a measurement length is chosen that isequal to the number of segments that will be used in the averaging ofthe spectral responses (step A). Each length is corrected for vibration(v) up to that point, strain (ε) present across the length is removed,and the measurement data set for this segment is compared to thereference data set for the correct segment of fiber in the baselinereference based on the delay signal (τ) (step B). The algorithm assumesthat these feedback signals v, ε, and τ are all determined duringinitialization within the processing of the OFDR system. The measurementlength is corrected using feedback signals v, ε, and τ at (step C). Asdescribed previously, vibration (v), can be removed by applying a phasecorrection to the spectral domain of the measurement that is based onthe distortion as a result of motion up to that location in the sensor.Strain (ε) across the measurement length is removed by applying a phaseslope across the data in the temporal domain that is proportional to thestrain. Misalignment in physical distance, or delay (τ), is accountedfor by indexing the baseline data according to this measure ofmisalignment. Once corrected, the measurement length is divided intosmaller segment measurement data sets (step D) to average the spectralphase response providing a robust measure of the effects of motion usingthe example techniques described above. The smaller segments allowmeasurement of a change in the distortion as a result of motion (Δv), achange in strain across the segments (Δε), and a change in the delaymismatch (Δτ) between the reference and measurement (step E). Thesechanges Δv, Δε, and Δτ are accumulated with the previous values v, ε,and τ to produce a new set of values v′, ε′, and τ′ (step F). Assumingthat the signals are slowly varying along the length of the sensor,these accumulated values v′, ε′, and τ′ are a good approximation of thenecessary signals needed to correct the next measurement length (G). Theprocessing is repeated moving along the length of the sensor fiberslowly removing and monitoring the change in strain along the fiber, thechange in accumulated distortion as a result of motion, and theaccumulated delay.

OFDR is a valuable technique for performing high resolution distributedstrain measurements. In many applications, it is desired to performmeasurements at a distance away from the measurement system. In somesituations of extreme environments, the instrument cannot be placed nearthe sensing fiber. As an example, if the sensing fiber was deployed in acryogenic chamber, the instrument could not be operated in the proximityof the sensing fiber. A length of fiber, such as a patchcord, would haveto be placed between the measurement and the sensing region of thefiber. The length of fiber between the measurement system and thesensing region of the fiber effectively serves as an antenna thatreceives both mechanical and acoustic disturbances. These disturbancesdistort the measurement in the sensing region of the fiber, greatlydiminishing the effectiveness of the OFDR measurement. The abovedescribed compensation technology allows a measurement to be performedat the beginning of a sensing region that can be used to remove thedisturbances received by the sensor fiber. As a result, OFDR measurementtechniques are more effectively deployed in a wide range of applicationsand environments.

Although various embodiments have been shown and described in detail,the claims are not limited to any particular embodiment or example. Noneof the above description should be read as implying that any particularmember, step, range, or function is essential such that it must beincluded in the claims scope. The scope of patented subject matter isdefined only by the claims. The extent of legal protection is defined bythe words recited in the allowed claims and their equivalents. Allstructural and functional equivalents to the members of theabove-described preferred embodiment that are known to those of ordinaryskill in the art are expressly incorporated herein by reference and areintended to be encompassed by the present claims. Moreover, it is notnecessary for a device or method to address each and every problemsought to be solved by the technology described, for it to beencompassed by the present claims. No claim is intended to invokeparagraph 6 of 35 USC § 112 unless the words “means for” or “step for”are used. Furthermore, no embodiment, feature, component, or step inthis specification is intended to be dedicated to the public regardlessof whether the embodiment, feature, component, or step is recited in theclaims.

The invention claimed is:
 1. An optical interrogation system formeasuring a parameter of a sensing light guide subjected to atime-varying disturbance, the optical interrogation system comprising:an optical interferometric interrogator; optical detection circuitrycoupled to the optical interferometric interrogator, the opticaldetection circuitry for detecting interferometric measurement signalsfor a length of the sensing light guide, where the sensing light guideincludes a series of segments with corresponding segment locations alongthe length of the sensing light guide; and data processing circuitryconfigured to perform operations comprising: receiving theinterferometric measurement signals from the optical detectioncircuitry, generating a measurement data set based on theinterferometric measurement signals, the measurement data set includinga plurality of data segments corresponding to the series of segments;transforming one or more data segments of the plurality of data segmentsinto a spectral domain to produce one or more transformed data segments;extracting a phase signal from the one or more transformed datasegments; determining a non-linear compensating signal from the phasesignal by removing a linear fit from the phase signal; and using thenon-linear compensating signal to compensate at least some portion ofthe measurement data set for the time-varying disturbance.
 2. Theoptical interrogation system of claim 1, wherein the phase signal isextracted from the one or more transformed data segments by unwrappingthe phase signal.
 3. The optical interrogation system of claim 2,wherein removing the linear fit from the phase signal includes removingthe linear fit from the unwrapped phase signal.
 4. The opticalinterrogation system of claim 3, wherein using the non-linearcompensating signal to compensate at least some portion of themeasurement data set for the time-varying disturbance includessubtracting the non-linear compensating signal from the measurement dataset.
 5. The optical interrogation system in claim 1, wherein extractingthe phase signal from the one or more transformed data segments includescomparing the one or more transformed data segments with a baseline dataset in the spectral domain.
 6. The optical interrogation system in claim1, wherein the optical interrogation system is an optical frequencydomain reflectometry (OFDR)-based system, and wherein theinterferometric measurement signals indicate back scatter amplitude as afunction of time along the sensing light guide.
 7. The opticalinterrogation system in claim 1, wherein the measurement data setincludes a reflective event, and wherein the data processing circuitryis configured to window data of the measurement data set around thereflective event.
 8. The optical interrogation system in claim 1,wherein the sensing light guide is an optical fiber, and wherein thedata processing circuitry is configured to compensate the measurementdata set for a strain on the optical fiber.
 9. The optical interrogationsystem in claim 1, wherein the data processing circuitry is furtherconfigured to perform further operations comprising: determining motion,temporal delay, and strain along the sensing light guide; andcompensating for accumulated motion, accumulated temporal misalignment,and accumulated strain along the sensing light guide.
 10. The opticalinterrogation system in claim 1, wherein the data processing circuitryis further configured to perform further operations comprising: dividingthe measurement data set into multiple measurement data segments;comparing each data segment to a corresponding reference data segment;determining a temporal delay that indicates an amount of misalignmentbetween compared reference data segments and data segments; and usingthe temporal delay to align reference data segments and data segments ina temporal domain.
 11. A method for measuring a parameter of a sensinglight guide subjected to a time-varying disturbance, comprising:detecting interferometric measurement signals for a length of thesensing light guide, wherein the sensing light guide includes a seriesof segments with corresponding segment locations along the length of thesensing light guide; and generating a measurement data set based on theinterferometric measurement signals, the measurement data set includinga plurality of data segments corresponding to the series of segments;transforming one or more data segments of the plurality of data segmentsinto a spectral domain to produce one or more transformed data segments;extracting a phase signal from the one or more transformed datasegments; determining a non-linear compensating signal from the phasesignal by removing a linear fit from the phase signal; and using thenon-linear compensating signal to compensate at least some portion ofthe measurement data set for the time-varying disturbance.
 12. Themethod in claim 11, wherein the phase signal is extracted from the oneor more transformed data segments by unwrapping the phase signal. 13.The method of claim 12, wherein removing the linear fit from the phasesignal includes removing the linear fit from the unwrapped phase signal.14. The method in claim 11, wherein extracting the phase signal from theone or more transformed data segments includes comparing the one or moretransformed data segments with a baseline data set in the spectraldomain.
 15. The method in claim 11, further comprising: using an opticalfrequency domain reflectometry (OFDR)-based system, wherein theinterferometric measurement signals indicate back scatter amplitude as afunction of time along the sensing light guide.
 16. The method in claim11, wherein the measurement data set includes a reflective event, andwherein the method further comprises: limiting the measurement data setto a window of interferometric measurement data around the reflectiveevent.
 17. The method in claim 11, wherein the sensing light guideincludes an optical fiber, and wherein the method further comprises:compensating the measurement data set for a strain on the optical fiber.18. The method in claim 11, further comprising: dividing the measurementdata set into multiple measurement data segments; comparing each datasegment to a corresponding reference data segment; determining atemporal delay that indicates an amount of misalignment between comparedreference data segments and data segments; and using the temporal delayto align reference data segments and data segments in a temporal domain.19. An optical frequency domain reflectometry system for measuring aparameter associated with an optical fiber subjected to a time-varyingdisturbance, the optical frequency domain reflectometry systemcomprising: an optical interferometric interrogator; optical detectioncircuitry coupled to the optical interferometric interrogator, theoptical detection circuitry for detecting interferometric measurementsignals for a length of the optical fiber, where the optical fiberincludes a series of segments with corresponding segment locations alongthe length of the optical fiber, wherein the interferometric measurementsignals indicate back scatter amplitude as a function of time along theoptical fiber; and data processing circuitry configured to performoperations comprising: receiving the interferometric measurement signalsfrom the optical detection circuitry, generating a measurement data setbased on the interferometric measurement signals, the measurement dataset including a plurality of data segments corresponding to the seriesof segments; transforming one or more data segments of the plurality ofdata segments into a spectral domain to produce one or more transformeddata segments; extracting a phase signal from the one or moretransformed data segments; determining a non-linear signal from thephase signal by removing a linear fit from the phase signal; determininga compensating signal from the non-linear signal; and using thecompensating signal to compensate at least some portion of themeasurement data set for the time-varying disturbance.
 20. The opticalfrequency domain reflectometry system in claim 19, wherein the dataprocessing circuitry is further configured to perform further operationscomprising: determining motion, temporal delay, and strain along theoptical fiber; and compensating for accumulated motion, accumulatedtemporal misalignment, and accumulated strain along the optical fiber.